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NBSIR 76-989

STABLE PRESSURE TRANSDUCER

Jack H. Colwell

Institute for Basic Standards

National Bureau of Standards

Washington, B.C. 20234

January 1976

Interim Report

Prepared for

Aerospace Guidance and Metrology Center

Newark Air Force Station

Newark, Ohio 43055

CCG/Army/Navy

US Axmy Metrology and Calibration Center

Redstone Arsenal, AL 35809

U. S. DEPARTMENT OF COMMERCE

Rogers C. B. Morton, Secretary

James A. Balcer, III, Under Secretary

Dr. Betsy Ancker-Johnson, Assistant Secretary for Science and Technology

NATIONAL BUREAU OP STANDARDS

Ernest Ambler, Acting Director

ABSWiCT

This report describes recent work on the development of the soliddielectric capacitive pressure transducer. The performance of the system

with an invar' sample holder is described. This device minimizes adiabatic

heating effects so as to shorten thermal equilibration times and simplify

thermostating. The temperature and pressure dependences of several nevj

materials are reported. The potential of one of these, bismuth germanium

oxide, as a transducer material in conjunction with AS2S3 is presented. The

possible use of doped-crystals for minimizing the temperature dependence of

the capacitors is discussed.
*
DfTRODUCTIOII

In our search for a stable pressure transducer vie are continuing with

the development of a capacitance gauge which uses hydrostat ically pressurized

solid dielectric capacitors. To circumvent the inherent tenperature dependence

of individual capacitors we are experimenting with a device where two different

capacitors, placed in opposite arms of the Vheatstone bridge measuring circuit,

are both within the pressure vessel. The resulting bridge balance gives the

ratio of the two capacitances.

R = C1/C2 (1)

The observed change of the ratio measurement vdth tenperature and pressure

1 dR 1 dCi 1 dC2

is

and

R dT Ci dT C2 dT

1 dR 1 dC 1

p

(2)

(3) dP Ci dP C2 dP

The appropriate capacitors for the pressure transducer are therefore, ones

having nearly identical temperature dependences but widely differing pressure

dependences. Capacitor pairs made from parallel and perpendicular cuts of

calcite (CaCOs) meet our basic requirements reasonably well so we have been

proceeding with the development and testing of a device using this material.

The calcite pair does have drawbacks so that the tenperature and pressure

dependences of capacitors made from other materials are continuing to be

measured in the hope of finding a better combination. Hie current status

of tMs work is presented.

EIVAR SAP4PLE ?IOLDER

The invar sample holder for the pressure transducer has been tested sr.i

found to be basically satisfactory. A picture of the partially disassemble!

sairple holder is shown v/ith the pressure vessel in Fig. 1. The purpose of this

device is to minimize the time requiredfor theiTnal equilibration after press"ire

changes and to sinplify the thermostating as much as possible. V/henever a

pressure vessel is pressurized, the contents of the vessel are conpressed er.d

their tenperature increases while the vessel itself is stretched and cools.

The idea behind the invar sairple holder is to equate these heating and cooling

effects so that the tenperature of the system will return to its original value

after thermal equilibrium is reestablished following a pressure change. The

amount of heating that occurs in a piece of material under compressive or tensile

stress is given by

Q = T V 3 AP,

where T is the average thermal expansion coefficient of the material for the

range of the pressure change, AP, and V is the average volume. Calculations

indicate that for siirple geometries the cooling that occurs when a vessel is Ir.-

temally pressurized would be equal in magnitude to the heating that would

occur upon externally pressurizing a piece of the same material having a vcl'-une

equal to the internal volume of the vessel. Since it is necessai^y to use oil,

which has a very large expansivity, as the pressurizing fluid, the majority of

the internal volume of the vessel has been filled with invar, which has a

particularly small expansivity. By limiting the amount of oil to 7% or 12 c:n^

of the internal volume of the vessel and filling most of the remaining space

with invar, we calculated that the average expansivity should equal that of rhe

steel vessel. Our experiments Indicate that these ideas are basically correct.

In Fig. 2_ Yie show the actual temperature change observed vjith the system

upon changing the pressure. The pressure vessel was effectively isolated from

the surroundings in an insulated container with a thermometer attached to the

outer surface of the pressure vessel. At the center of the figure is shown

the effect of depressurizing the vessel over about a 1 minute period from

l40 r^Pa (20,000 psi) to zero. The outer surface of the vessel first vrams

but as the vessel thermally equilibrates with the material inside, it cools,

stopping at a tenperature h mK below the initial temperature. To the right

is seen the reverse effect when the system was repressurized. The slope of the

base line in the figure is due to small loss of heat to the surroundings. \le

calculate that each cm^ of oil in the system that is displaced by invar will

produce a 3 niK difference in the temperature change observed with a l40 MPa

pressure change. The results in Fig. 2_ indicate that 1 1/3 cm^ more oil needs

to be displaced from the system to exactly balance the heating and cooling

effects. To get to this point it was necessary to displace much more oil than

predicted by the calculation. In Fig. 3_ we have plotted the temperature changes

observed with three different quantities of oil in the system and find that

the temperature changes are varying as predicted but are displaced from the

calculated curve by nearly 8 cm^ of oil. Although it is not easy to determine

the exact amount of oil in the system, (considering screw slots, counter sitilcs,

oil equivalent of the 0-ring seal, etc.) we do not think we are in error by

this amount. The volume differences between the plotted points in Fig. 3 are

accurately Icnown, however, for they were determined by the volume of the im-ar

pieces used to displace successive quantities of oil. The most likely cause

of the discrepancy is our failure to properly account for the heating effects

of the threaded vessel closure. Our calculation assumed that the vessel has

spherical ends which when pressurized would be under a net tensile stress.

The threaded closure of the actual vessel, however, will be under largely

corrpressive stresses. This oversight is unfortunate for in designing the

sample holder v;e were overgenerous in the size of the openings allowed for

various purposes and they will be difficult to modify.

Another, and potentially more serious problem is that in attempting to

use the invar sanple holder, we have repeatedly broken the calcite capacitors

when changing the pressure in the system. The problem appears to be due to

poor flow patterns for the oil in the system so that any pressure surge

develops large pressure gradients across the crystals. The main path for the

flow of oil in the system is the hole along the central axis of the sar.ple

holder. This hole communicates directly vri.th the inner surface of the

capacitors and probably results in a large pressure gradient across the

capacitor. By blocking off this path and forcing the oil to enter the sample

chambers at the edge of the capacitors we may be able to get around the

I

I problem. It is only the calcite crystals with the crystalline axis parallel

to the faces that have been breaking. These crystals are particularly susceptible to any abuse because of the cleavage planes which lie normal to the

faces of the discs. In trying to determine the cause of the breakage \':e

exhausted our supply of these crystals and are just now getting back to the

testing of the device.

NEVJ MATERIALS

The terrperature and pressure dependences of capacitors made from

several new dielectric materials are given in Table 1 and are plotted in Fig. k

along with the values of materials measured earlier.

T^ble I

Material Dielectric

Constant

i§.x lO'VPa i § X lOS/K

CaP2-3^ER3+

LiTaOg-X

LiTaOg-Z

BGO(Bii2Ge02o)

Diamond

Te02(100)

Te02(001)

5.6

54

44

46

5.9

23

27

-50.4

-47.1

-27.7

-102.5

- 1.444

+ 22.8

- 38.0

182

165.6

1302.5

72.0

9.2

151.0

255.5

The measurem.ent of all but the erbium-doped CaF2 sample was made possible

by the development of techniques for handling sairples smaller than the usual

1" discs. The LiTaOa and BGO (bismuth germanium oxide, Bii2Ge02o) samples

were 3/4" discs and the Te02 (paratellurite) samples were discs.

The diamond sanple was a triangular plate measuring approximately 3/8" by 1/2".

Masking rings for the aluminum electrode coatings \\'ere 1/2" diameter for the

3/4" discs and 0.350" for the smaller samples. The diamond and doped CaF2

sanples were obtained from John Fontanella of the U.S. Naval Academy, the others

were fr-om commercial sources . Two of these new materials, BGO and the doped

CaP2, are of particular interest and are discussed in detail below.

BGO

' Bismuth germanium oxide (Bii2'^e O20) is a pale yellow material that is

commercially available as discs cut from optically clear single crystals. The

sanple used in our present measurements was of obviously poor quality; the

highly polished disc of 0.024" thickness was not transparent. This is of

inportance since there was a drift in the capacitance which lasted for

i several hours following a temperature or pressure change. The total change

during these periods of drift was small but amounted to an equivalent

pressure change of the order of 10^ Pa (tens of psi). Be.ha,vior of this

type has been observed in two classes of materials, those that are impure

and those that are either piezoelectric or pyroelectric such as quartz or

LiTaOa . BGO is piezoelectric so the observed drift may be associated with

that property rather than the obvious poor quality of the present sample.

Our interest in BGO stems from its tenperature dependence being close

to that of AS2S3 while the pressure dependence of the two materials are

large and of the opposite sign. The properties of these two materials are

plotted in Fig. 4 where their relation to other materials can be seen and in

Fig. 5 where their relation to each other is detailed. AS2S3 samples from

three different sourceswere measured and there is some variation between them

as shown in the figures. In Table 2 the coefficients are tabulated for the fit

of the experimental results to the equation, ,

C=Co(l + AP + BP2) . (5)

These are listed with a few other examples for conparison. As2S3(B) values

are used in the table. At the bottom of Table II are listed the coefficients

that could be realized \^fith an AS2S3-BGO pair combination as well as those of

a calcite pair.

i

I Table II Temperature and Pressure Characteristics of Capacitors

'aterial

1

C° \JL J. 1^ AxlO^VPa ^lO^VPaK)

0.-1-

1 dA

( 1)

A dT

BxlO^O

262 -37.8 -0.025 0.00066 0.27

:aC03X 331.5 12.0 0.0149 0.00124 0.42

^aCOa 11 335 71.0 0.0169 0.00024 1.25

M2S3 67 116 0.047 0.00040 -1.36

BGO(Bii2GeO 20) 72.0 -102 0.037 0.00036 1.8

Pair Combinations

•laterials |og°xl0VK |o §"=Axl0iVPa ^lOiV(PaK)

CaCOs Pair 3-6

.HS2S3-3GO -5

59.0

218

0.0020

0.004

A dT^^ ^

0.000034

0.000018

ExlO^VPa^

0.76

-3.4

The data for the pairs can be used to determine the thermostating

requirements one would face in utilizing an AS2S3-BGO pair compared to a

calcite pair. There are three v/ays a capacltive pressure determination can be ,

influenced by temperature effects. They, are: (1) lack of thermal equilibrium

between the two capacitors, (2) the capacitance measurement under pressure

being made at a different temperature from that of the reference value at

zero pressure (see Ecjn, 5), and (3) the absolute temperature being in error

since the coefficient of Fm . 5 are temperature dependent . The equations for

determining the effect of these errors were presented in the April, 1975 report

on this project. A conparison of the allowable thermal variations for the

two capacitor systems are presented in Table III, The considerable improvement

achievable with the AS2S3-EGO pair is evident.

Table III Thermal stability required to obtain 700 Pa (0.1 psi)

pressure resolution with calcite pair and AS2S3-BGO

capacitor combinations

.

Materials

Thermal equilibrium

between capacitors

Short term Long term,

temperature precision^ temperature accui":

0 -> 1^0 MPa At l40 MPa

CaC03 pair 0.12 mK 11.5 10 mK 75 mK

AS2S3-BGO 2.2 mK 30 ^ 39 mK 140 mK

We have ordered some high quality BGO sanples and plan socnto test

whether or not the drift behavior observed vr!th our present sanple Is ^n

intrinsic property of the material or due to lirpurltles In our sample.

Erbium doped CaF2

John Fontanella and Carl Andeen have been conducting experiments on

erbium doped calcium fluoride crystals. Their Interest Is primarily in the

dipolar conplexes formed by Er^"^ doping, but the experlm.ental results

Indicate that it may be possible to produce a capacitor having a low

temperature dependence in this way. In Fig. 6_ we have reproduced a figure

from a paper they have recently submitted to Journal of Physics, C which

shows the temperature variation of the dielectric constant of several

CaF2- Er^"*" crystals. The lowest curve in the figure effectively represents

the behavior of undoped CaF2. The two highest curves at 1 and 3^ Er^"^ are the

curves of interest, they show minima, i.e. zero temperature dependence, at

tenperatures of about 100 and 200 K, respectively. If by increasing the level

of doping, the minimum could be raised to 300K the material would be well

suited for a capacitive pressure transducer.

We have made capacitance measurements with the Bp Er^"^ CaF2 sanple as a

function of temperature and pressure and found the system well behaved. The

loss component v/as up by about a factor of 50 over the pure material but was

still at a tolerably low level. From the trend of the loss component with

increasing Er^"*" doping, however, one would predict that the loss may become

too large at concentrations greater than yjo so that it may be necessary to

use a different doped system to fully exploit this approach. These ideas

will have to be verified by experiment.

Capacitance Bridge

The limited-range automatic capacitance bridge being built for use v/ith

the pressure transducer has been essentially conplete for several months but

corrponent failures have prevented us from testing it with the pressure

transducer. The main problem has been with the voltage-to-frequency converters

which failed, were repaired and failed again. The manufacturer could give

no reason for the repeated failures and the components have been replaced

with new models.

Figure Captions

1. Invar sample holder and pressure vessel.

2. Temperature changes at the outer surface of the isolated pressure

vessel resulting from 1^0 Wa (20,000 psi) pressure changes.

Vessel contains the invar sanple holder and about 5 cm^ of

pressurizing oil. Central peak is for decreasing pressure to

zero and peak at right is for repressurizing.

3. Net temperature changes in isolated transducer system containing

different quantities of oil.

4. The pressure dependence of the capacitance of various materials

as a function of their temperature dependence. The values given

are for 35°C and atmospheric pressure. The lines joining sanples

of different crystalline orientation indicates values that could

be achieved at intermediate angles.

5. The temperature and pressure dependence of BOO (Bii2Ge O20) 3oad. AS2S3. Three different samples of AS2S3 sanples were measured

(A) Servo Corporation, (B) Barnes Engineering, and (C) an older

Servo Corporation sanple supplied by John Fontanella. Arrov;s

indicate how the dependences change under a pressure of l40 I-Tsl.

6. The real part of the dielectric constant of several Er^"^ doped

CaF2 crystals as a function of temperature. Top curve is a 3%

sample, the next is 1% and the loviest is 0.001^. The results

were obtained by John Fontanella and Carl Andeen and are to be

published in Journal of Physics, C.